Chaotic time dependence in a disordered spin system

L. R.G. Fontes, M. Isopi, C. M. Newman

Research output: Contribution to journalArticlepeer-review


Stochastic Ising and voter models on ℤd are natural examples of Markov processes with compact state spaces. When the initial state is chosen uniformly at random, can it happen that the distribution at time t has multiple (subsequence) limits as t → ∞? Yes for the d = 1 Voter Model with Random Rates (VMRR) - which is the same as a d = 1 rate-disordered stochastic Ising model at zero temperature - if the disorder distribution is heavy-tailed. No (at least in a weak sense) for the VMRR when the tail is light or d ≥ 2. These results are based on an analysis of the "localization" properties of Random Walks with Random Rates.

Original languageEnglish (US)
Pages (from-to)417-443
Number of pages27
JournalProbability Theory and Related Fields
Issue number3
StatePublished - Nov 1999


  • Chaotic time dependence
  • Disordered spin system
  • Random environment
  • Random walk
  • Stochastic Ising model
  • Voter model

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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